The Frequency sampling approach to designing FIR filters is conceptually the simplest approach to FIR filters. Unfortunately it is also the most tedious to apply. The images below and the applets on the following pages attempt to show why this is the case.

In principle, the proceedure is as follows.

First determine the frequency response of the desired filter LP, HP etc.

Next sample this frequency response with the number of samples being equal to the length of the desired FIR filter.

Now use the IDFT of the frequency samples to find the Impulse response of the filter.

Using the impulse response and the Z transform, plot the DTFT frequency response of the impulse response and verify that the resulting frequency response is close enough to the desired frequency response. If not then adjustments will need to be made to the desired frequency response using transition samples or to the impulse response using windows in order to get an acceptable frequency response.

The Impulse response of an Ideal low pass filter is:-

The next 2 images attempt to show why this method can become very tedious. In the first image one sees that the frequency response calculated from the impulse response shown in green passing smoothly through the samples shown by the red x's. This happens provided the desired frequency response does not have major discontinuities in its value or its derivatives.

COPYRIGHT © 2008 Cuthbert Nyack.